6a. Let V be a finite dimensional space, and let Land T be two linear maps on V. Show that LT and TL have the same eigenvalues.

6b. Show that the result from part A is not necessarily true if V is infinite dimensional.

Suppose you were designing two experiments to measure the same quantity “Y”. Through analysis of both experimental systems, found; Experiment 1, Y depends on a X2 , and for Experiment 2, Y depends on Z4. Here, “X” and “Z” are names of variables that you can measure in the lab. If you have the same amount of resources to perform and equal number of measurements, which experiment should you perform (there is a correct answer here!). Explain your rationale

There are 7 balls in a bag. They are identical except for color. 3 are red, 2 are white and 2 are blue. You are to draw 1 ball from the bag, note its color, and set it aside. Then you are to draw a second ball from the bag and note its color.

a. Make a tree diagram to show all possible outcomes of the experiment. Label the probability associated with each stage of the experiment on the appropriate branch.

b. Compute the probability for each outcome of the experiment.

A professor believes that students who have the opportunity to write their essays on word processors will produce better essays than those who write them by hand. Design an experiment that tests this idea.

1. Do you need to define any terms for your experiment (operationally define)? If so, define them here.

2. What purpose would this line of research serve (and which subgroup do you think this experiment would most closely relate with)?

Plant asset accounting: During 2016 and 2017, ABC Corporation experienced several transactions involving plant assets. A number of errors were made in recording some of these transactions. For each item listed on the attached file, indicate the effect of the error (if any) using the following codes:                        O = Overstate; U = Understate; NE = No Effect *

*If no error was made, write NE in each of the four columns.

Interest cost qualifying for capitalization in 2016 was charged to interest expense in 2016.

For H₂O, determine the specified property at the indicated state.

(a) T = 140°C, v = 0.5 m³/kg. Find p, in bar.
(b) p = 30 MPa, T = 120°C. Find v, in m³/kg.
(c) p = 10 MPa, T = 450°C. Find v, in m³/kg.
(d) T = 80°C, x = 0.8. Find p, in bar, and v, in m³/kg.

1. The following data were collected in a kinetics experiment for the disproportionation of A₂ in a buffered solution: 3 A₂ -> products

The "generic" rate law for the reaction is rate = k[A₂]^p

Plot the data according to the method described in this experiment to determine p, the order of the reaction with respect to A₂. (Hint: The reaction order is not a whole number. Round the order to 2 significant figures.) ****I think the initial concentration of A₂ must be calculated from the data given?? I am not sure how to proceed. This is all the information I have. *****

5. How is the order of the reaction with respect to H₂O₂ determined in the experiment

a. chemically?

b. graphically?

6. Explain how the rate constant, k^', is determined for the rate law in the experiment.

7. Explain how the activation energy, E_a, is determined for the reaction in the experiment.

Create a program named DiceGame.Java (in Java lagnuage of course)

The problem/background info: Suppose someone comes to you and says “I have a 6-sided Die and different one that has 4 sides. Both are fair dice. I would like to propose a game. We will roll both dice and I will give you $3.00 if the total is less than 5 and $8.00 if the total is exactly equal to 5. But if the total is greater than 5, you give me $2.00.”   Should you do it? Should you do it if the second die had 6 sides?

Your program will simulate this:   You are given a class called Die, which has a default constructor (makes it 6-sided) and has a parameterized constructor that accepts a number of sides (minimum 4 sides or else it will throw an exception).   It also has a method called roll() which rolls itself and returns the (int) result; it also has a method called getNumSides() which returns the (int) number of sides it has.   You will write a program called DiceGame.java that simulates running the game over and over by doing the following:

• Ask the user how many sides the second die should have; store the response.
• Ask the user how many times to roll the dice; store the response.
• Ask the user how often to print the results; store the response.
• Ask the user to enter their name and store the response. Their name can have spaces in it.
• Create a 6-sided die to use.
• Create a die with as many sides as the user entered (using its parameterized constructor) to use.
• Skip a line (use \n in your next output to do this) and then print “Experiment by: “ and then their name.   But…if their name has more than 5 characters, then just print first 5 characters of the name; otherwise print the whole name.
• Tell both dice to roll themselves as many times as the user said to. As this is happening,
  • At every roll, add up the dice results, calculate the “winnings,” and keep track of how much money you have won or lost since the game began. The money should look like money (see below for how to do this).
  • Every n rolls, print the number of rolls that have occurred so far and the average money won/lost (total divided by number of rolls so far). n here is how often the user said to print the results. See the example below for the exact format.
• After all the rolls are finished, print the final number of rolls and the average money won/lost (total divided by number of rolls).

Notes:

• Don’t forget to flush the extra ENTER from the input stream (the program has .nextInt followed by .nextLine). For maintainability, that statement deserves a comment to explain why it is there.
• Be sure that your output lines contain the exact wording; otherwise the tester will not pick up the line.
• There should be a tab before the words “Average winning per roll:”
• When looping n times, programmers generally use a for loop where i starts at 0 and keeps going while i
• To make a result look like money, create an instance of the NumberFormat class, like this:

NumberFormat money = NumberFormat.getCurrencyInstance();

                ( you will have to import java.text.NumberFormat; )

            Then use your instance whenever you print your_calculation, like this

                                System.out.println(money.format(your_calculation));

                When formatted, negative money will be in parentheses rather than having a minus sign.

// This class will simulate a Die (half a pair of dice)

public class Die

{

//------- data

private int numSides;

private java.util.Random rGen;

//------- constructors

public Die()

{

this(6); //call parameterized constructor, as if 6 were passed in

}

public Die(int theSides)

{

if (theSides < 4)

throw new IllegalArgumentException("A Die cannot have less than 4

sides");

numSides = theSides;

rGen = new java.util.Random(numSides);

}

//------- methods

//getNumSides - returns the number of sides

public int getNumSides()

{

return numSides;

}

//roll - returns a random number from 1-numSides. The seed for the

random number generator should be the numSides

// (so everyone's results are the same...)

public int roll()

{

return rGen.nextInt(numSides) + 1;

}

}

Example1:

How many sides should the second die have?

4

How many times should we roll the dice?

87654

How often should we print results?

10000

What is your name?

Stephanie

Experiment by: Steph

Rolls: 10000    Average winning per roll: $0.90

Rolls: 20000    Average winning per roll: $0.91

Rolls: 30000    Average winning per roll: $0.92

Rolls: 40000    Average winning per roll: $0.91

Rolls: 50000    Average winning per roll: $0.92

Rolls: 60000    Average winning per roll: $0.91

Rolls: 70000    Average winning per roll: $0.91

Rolls: 80000    Average winning per roll: $0.91

Rolls: 87654    Average winning per roll: $0.91

Example2:

How many sides should the second die have?

6

How many times should we roll the dice?

400

How often should we print results?

100

What is your name?

Joe

Experiment by: Joe

Rolls: 100      Average winning per roll: ($0.45)

Rolls: 200      Average winning per roll: ($0.30)

Rolls: 300      Average winning per roll: ($0.37)

Rolls: 400      Average winning per roll: ($0.33)

Rolls: 400      Average winning per roll: ($0.33)

19. a. For the titration of 50.00 mL of 0.0500 M Fe2+ with 0.1000 M Ce4+ in the presence of 1 M H2SO4, please calculate the system potential after 2.25 mL of Ce4+ is added .

Ce4+ + e ÍÎ Ce3+, E0 = + 1.44 V (in 1M H2SO4)

Fe3+ + e ÍÎ Fe2+, E0 = + 0.68 V (in 1M H2SO4).

They got Esystem = 0.62 V.

b)  For the same titration as in question (a), what’s the system potential after 32.00 mL of Ce4+ is added?

Answer: Esystem = 1.41 V

c) If we set up an electrochemical cell where the cathode is the system that we have in question (b), whereas the anode is a saturated calomel electrode (0.2444 V relative to standard hydrogen electrode). Please determine the potential of this electrochemical cell.

Answer: Ecell = 1.16 V

d) Please determine the system potential at the equivalence point for the titration described in question (a).

Answer: Esystem = 1.06 V

I listed all the answers. I just want to see how they got that. Thanks.

Determine if ~w = (−4, 6, 1) is a linear combination of ~u = (1, 0, −1) and
~v = (1, −11, 3) . If so, then express ~w as a linear combination of ~u and ~v .

Let ~u = (1, 1, −1) and ~v = (2, 1, 3). Determine if ~w = (7, 6, 3) is a linear
combination of ~u and ~v. If so, express ~w as a linear combination of ~u and ~v.

Let
~x1 = (2, −1, 3, 1), ~x2 = (1, 0, −1, 1), ~x3 = (0, 1, 4, 2).
(i) Determine if ~x1, ~x2, and ~x3 are linearly independent. Justify your answer.
(ii) Determine if ~v = (2, −1, 3, 1) is a linear combination of ~x1, ~x2, and ~x3.
If so, express ~v as a linear combination of ~x1, ~x2, and ~x3. If not, justify
your answer.
(iii) Determine if ~u = (1, 0, 0, 1) is a linear combination of ~x1, ~x2, and ~x3. If
so, express ~u as a linear combination of ~x1, ~x2, and ~x3. If not, justify
your answer.